Scatter butter pieces over flour mixture, tossing to coat butter with a little of the flour. Pulse machine 5 times in 1 second bursts. Add shortening and continue pulsing until flour is pale yellow and resembles coarse cornmeal, with butter bits no larger than small peas, 4 to 6 more 1 second pulses. Turn mixture into medium bowl. If you don't have a food processor, grate frozen butter and shortening into flour mixture and mix with your hands for 1 minute, rubbing flour and shortening between your fingers. Flour should turn very pale yellow and become coarser in texture.

Sprinkle 6 tablespoons of ice water over mixture. With blade of rubber spatula, use folding motion to mix. Press down on dough with broad side of spatula until dough sticks together. Shape into ball with hands, divide the dough into two balls one sightly larger than the other. Dust lightly with flour, wrap separately in plastic and refrigerate for at least 30 minutes.

Remove dough from refrigerator. The dough is ready to be rolled when it is still cool to the touch but you can push your finger halfway down through the center. If the dough has been chilled for more than 1 hour, it may have to sit on the counter for 10 to 20 minutes to soften.

Heat oven to 425 degrees.

Roll larger dough disk on lightly floured surface into a 12-inch circle, about ⅛-inch thick, the depth of a quarter. Transfer and fit dough into 9-inch Pyrex pan, leaving dough that overhangs the lip in place. Refrigerate dough while preparing the fruit.

Turn fruit mixture, including any juices, into pie shell. Roll out the remaining ball of dough and place it over the top of the pie. Trim top and bottom edges to ½-inch beyond pan lip. Tuck this rim of dough underneath itself so that folded edge is flush with pan lip.

Flute dough in your own fashion, or press with fork tines to seal.

Cut four slits at right angles on dough top to allow steam to escape.

Brush egg white on top of crust and sprinkle 1 tablespoon of sugar evenly over the top.

Place pie on bottom rack. Bake until crust is lightly golden, 25 minutes. Reduce oven temperature to 375 degrees and continue to bake until juices bubble and crust is deep golden brown, 30 to 35 minutes.

The bottom crust should be golden and the juices from pie bubbling.

Transfer pie to wire rack: let cool to almost room temperature about 4 hours. Pie is best eaten after it has completely cooled, even the next day.